A postman delivers mail daily starting on Day 1. The conditional probability that he is bitten by a dog onDay n, given that he has not been bitten on any of the preceding days, equals qn. Let X be the number ofdays until the postman sustains his first bite (i.e., the first bite occurs on Day X).(a) Write an expression for P(X > n) in terms of qi’s.(b) Write an expression for P(X = n) in terms of qi’s.For the remainder of the problem, let qn = α for all n, where 0 < α < 1.(c) What is the probability that the postman is never bitten by a dog? Justify your answer.
Answers
The probability that the postman is never bitten by a dog is equal to the product of all qi's from i=1 to infinity, which is equal to (1-α)^∞. This is equal to 0 since α is a positive number.
The probability that the postman is never bitten by a dog is given by P(X > n), where X is the number of days until the postman sustains his first bite. This probability can be expressed as the product of all of the qi's from i=1 to n, which is equal to (1-α)^n, where qn = α for all n, and 0 < α < 1. The probability that the postman is never bitten by a dog is equal to the product of all qi's from i=1 to infinity, which is equal to (1-α)^∞. Since 0 < α < 1, (1-α)^∞ is equal to 0, meaning that the probability that the postman is never bitten by a dog is 0. This is because as n increases, the probability that the postman is not bitten by a dog on Day n decreases, and as n approaches infinity, it approaches 0.
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Related Questions
{ (-2, 4), (0, 2), (-1, 3), (4, -2)}
The set of ordered pairs above:
DONE
Domain
-3
4
-1
5
Range
3
7
-2
The mapping diagram above:
DONE
y=x²
DONE
x
-3
-1
y
5
2
-1
The table above:
DONE ✔
Answers
The set of ordered pairs above: is a function.
The mapping diagram above: is a function.
y = x²: is a function.
The table above: is not a function.
What is a function?In Mathematics and Geometry, a function is a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.
Based on the set of ordered pairs, mapping diagram, and the equation above, we can reasonably infer and logically deduce that it represent a function because the input values (domain, x-value, or independent values) are uniquely mapped to the output values (range, y-value or dependent values).
In this context, we can reasonably infer and logically deduce that the table does not represent a function because the input value (-1) has more than output values (2 and 4 respectively).
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How many moles are 1.20 x 1025 atoms of phosphorous?
Answers
Answer:
19.93 moles
Step-by-step explanation:
I NEED HELP WITH STATISTICS
Answers
A. The null hypothesis H₀ and the alternative hypothesis H₁ are:
H₀: μ = 35 minutes H₁: μ > 35 minutes
B. If the consultant decides not to reject the null hypothesis, she might be making a Type II error.
C. A Type II error would be failing to reject the hypothesis that μ is = to 35 minutes when, in fact, μ is 43 minutes.
What is a Type II error?A Type II error occurs when the null hypothesis is false, but the test does not reject it.
In this case, the consultant would be concluding that the mean shopping time is 35 minutes, when in fact it is greater than 35 minutes.
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If the graph of an equation is a vertical line, what can you say about the solutions of that equation, and why
Answers
The equation x = 3 represents a vertical line that intersects the x-axis at the location (3,0). A solution is any ordered pair with 3 as its first coordinate.
We know that the x value is the same for each point on the vertical line, the equation is simply x = that number, such as x = 3.
Remember that if a line is parallel to an axis, the axis letter will not appear in the equation. When an equation contains both x and y, it is not parallel to either axis and will cross both.
Thus, the equation x = 3 represents a vertical line that crosses the x-axis at the point (3,0). Every ordered pair with 3 as its first coordinate is a solution.
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Solve and then graph solution on umber line
y-5>-2
Answers
Answer:
Start from -2 on the Y axis then go down 5 and right 1
Step-by-step explanation:
Find n so that mean of the data set is 140. (120, 145, 130, 80, 95, 100, 340, n)
Answers
Answer:
Answer: n is 110
Step-by-step explanation:
Formular:
\(mean = \frac{ \sum(n_{1}, \: n _{2}, \: ...n_{n} ) }{n} \\ \)
therefore:
\(140 = \frac{(120 + 145 + 130 + 80 + 95 + 100 + 340 + n)}{8} \\ \\ (8 \times 140) = 1010 + n \\ 1010 + n = 1120 \\ n = 1120 - 1010 \\ n = 110\)
12x + 3y = 15
Solve &Justification
Answers
Answer:
Step-by-step explanation:
12x+3y= 15
12x= -3y+15
divide both sides by 12 and you get
x= -3/12y+15/12
simplifying:
x=-1/4+5/4
What are 2 ratios equivalent to 3:12
Answers
Answer:
6/24
Step-by-step explanation:
Well, this ratio would be written as 6/24. Using your knowledge of equivalent fractions, you can see that 3/12 = 6/24 (multiply the numerator and denominator of 3/12 by 2 and you get 6/24.
Hope this helps you.
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Assume moe's southwest grill has a break-even point of 24,000 units. At this point, total sales are $1,800,000 and total variable costs are $1,200,000. Compute total fixed costs at the break-even point. I know the answer is 600,000 but I want to know how to solve it. Please answer
accounting only please answer
Answers
Answer:
Fixed Costs = $600,000
Step-by-step explanation:
Total Sales = $1,800,000
Unit price (UP) = $1,800,000/24,000 units = $75
Total Variable Cost = $1,200,000
Variable Cost per unit (VC)= $1,200,000/24,000 units = $50
Break-even Point ( in units) = 24,000
Break-even point (Q) = Fixed Costs/ [UP - VC]
24,000 = FC / [$75 - $50]
24,000 = FC / [$25]
Multiply both sides by $25 to isolate FC:
24,000 ($25) = [FC / $25] $25
$600,000 = Fixed Cost
Which graph indicates decreasing speed?
A. Graph c
B Graph A
c graph F
d graph
Answers
pls pls pls pls pls pls pls pls pls pls pls pls pls pls help
Answers
Answer:
69 miles
Step-by-step explanation:
53 + 16 = L
69 = L
Kate hiked 14 miles in 6 hours.
Which rate represents the number of miles traveled per hour?
Answers
Answer:
Step-by-step explanation:
To answer this, look at the form of the answer. they want miles per hour. So, just do that calculation
She traveled 14 miles in 6 hours.
14 miles/6 hours
14/6 = 7/3 = 2.3333 miles/hour
Which expression is equivalent to 7a + 2a + 7 - a-2
Answers
Answer:
8a+5
Step-by-step explanation:
find the equation of the line passing through points A(3,4) and B(1,10)
Answers
Answer:
y = -3x + 13
Step-by-step explanation:
First, find the slope:
\(m=\frac{y_1-y_2}{x_1-x_2}\\\\m=\frac{4-10}{3-1}\\\\m=\frac{-6}{2}\\\\m=-3\)
Finally, find the equation:
\(y-y_1=m(x-x_1)\\\\y-4=-3(x-3)\\\\y-4=-3x+9\\\\y=-3x+13\)
9x-(3x-3)=21
Solve the equation. Select the correct choice below and if necessary, fill in the answer box to complete your choice. The solution set is (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.) The solution is all real numbers. The solution is the empty set.
Answers
Prove that the difference between 9th square number and 5th square number is a multiple of 8?
Answers
Answer:
Step-by-step explanation:
9th square number = 81
5th square number=25
81-25=56
56 is a multiple of 8 as 8 x 7=56
The product of 46 and a number added to the reciprocal of a number squared.
Answers
The expression for the given word phrase is
46M + M² + 2 + 1/M²
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number = M
Reciprocal of M = 1/M
Now,
46 x (M + 1/M)²
Step 1:
46M + M² + 2 + 1/M²
Thus,
The expression is 46M + M² + 2 + 1/M²
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Identifying a pattern cannot help you make an estimate.
True or False
Answers
Answer:
false i think
Step-by-step explanation:
What property is 4(2+c)+5
Answers
The radius, R, of a sphere is 7.8 m. Calculate the sphere's volume, V.
Use the value 3.14 for , and round your answer to the nearest tenth. (Do not round any intermediate computations.)
Answers
Answer:
1986.8m³
Step-by-step explanation:
Radius=7.8m
Volume of sphere =4/3pi r³
=4/3×3.14×7.8³=1986.8m³
work out the area of this circle take pi to be 3.142 and write down all the digits given by your calculator diameter 13cm
Answers
Area of circle of diameter with 13cm is 132.74
What is area of circle?
The space a circle takes up in a two-dimensional plane is known as the area of the circle.Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. A = r², where r is the circle's radius, is the formula for calculating a circle's surface area. The square unit—for instance, m², cm², in², etc.—is the unit of area. In square units, the area of a circle is equal to r² or d²/4 where (Pi) = 22/7 or 3.14. The ratio of a circle's circumference to its diameter is known as pi (). This unique mathematical constant exists.Given :
Diameter of circle, d = 13cm
Radius of a circle, r = d/2
=13/2
=6.5
Area of circle = πr²
= 3.142 * 6.5 * 6.5
= 132.74
Hence, the Area of circle of diameter with 13cm is 132.74.
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What point is closest to x axis
Answers
Answer:
7 is the smallest number making it the closest to the x- axis.
Step-by-step explanation:
Simplify -4x^5- 42x^5
Answers
Answer:
\( - 4x {}^{5} - 42x {}^{5} \)
\( = ( - 4 - 42)x {}^{5} \)
\( = - 46x {}^{5} \)
Which expression is equivalent to 5–√3⋅4–√5
5
3
⋅
4
5
?
Answers
The expression that is equivalent to ∛ 5 * \(\sqrt[5]{4}\) is \(5^{1/3}*4^{2/5}\)
What are radicals in math?A radical in mathematics is the opposite of an exponent, which is symbolized by the sign "n√" also known as root.
The number before the symbol or radical is regarded as an index number or degree, and it can either be a square root or a cube root and so on.
How to find the equivalent expressionThis equation represents exponents in fraction form and the basics for the calculation is from
x^(b/n)
\(\sqrt[n]{x}^{b}\)
Rewriting the expression is done as below
∛ 5
= \(5^{1/3}\)
and
\(\sqrt[5]{4}\)
\(= 4^{2/5}\)
combining both gives
∛ 5 * \(\sqrt[5]{4}\)
\(5^{1/3}*4^{2/5}\)
\(5^{1/3}*4^{2/5}\) is the equivalent expression
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Lauren has a garden in the shape of a rectangle where the length is 5.4 meters and 1.5 meters. She plans on increasing both the length and width by 40%
Answers
Answer:
5.4 = 7.56
1.5 = 2.1
Step-by-step explanation:
Just find the answer for 40% of the given meters.
a computer that normally cost 500 dolars was on sale for 200 dollars. what is the percent decrease. please show work for brainlist
Answers
Answer:
(100/500) *200 =40%
Step-by-step explanation:
If a covert promoter charges $65 per ticket for a concert. The promoter’s cost will be $5500 plus $4 per ticket. Write an equation for the profit function
Answers
the equation will be 61n - 5500
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
If a covert promoter charges $65 per ticket for a concert. The promoter’s cost will be $5500 plus $4 per ticket.
Here it is: r(n) - c(n)
which goes to
65n - (4n + 5500)
=61n - 5500
Hence, the equation will be 61n - 5500
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Fill in the table using this function rule.
y=-3x-3
X
-2
-1
0
1
y
0
0
0
X
Ś
Answers
Answer:
X | y
---------------
-2 | 3
-1 | 0
0 | -3
1 | -6
I don't understand this, help me?
Answers
Answer:
Hello' I think you forgot to add a picture
Please read question and know that the shape is in feet not inches and we are trying to figure out how many cubic yards of soil is needed to fill the bed to a depth of 30in please be as accurate as possible and round up to the nearest yard as needed
Answers
First we divide the figure into 3 rectangles and find the volume of each one. This is:
Then, the volume for rectangle 1:
Given, depth of 30 in
\(30in\times\frac{1ft}{12in}=2.5ft\)The volume formula is
\(V=lwh=15\times5\times2.5=187.5ft^3\)Volume for rectangle 2:
\(V=16\times4\times2.5=160ft^3\)Volume rectangle 3 = Volume rectangle 1:
\(V=187.5ft^3\)Therefore, the volume of the figure is:
\(V=187.5+160+187.5=535ft^3\)Next, we have:
1 yard = 3 ft
So 1 cubic yard is given by
\(1yd^3=3\times3\times3=27ft^3\)Hence:
\(V=535ft^3\times\frac{1yd^3}{27ft^3}=\frac{535}{27}yd^3=19.81yd^3\)Round up the nearest yard = 20 cubic yard
Answer: 20 cubic yards
